ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  pwex GIF version

Theorem pwex 4077
Description: Power set axiom expressed in class notation. (Contributed by NM, 21-Jun-1993.)
Hypothesis
Ref Expression
pwex.1 𝐴 ∈ V
Assertion
Ref Expression
pwex 𝒫 𝐴 ∈ V

Proof of Theorem pwex
StepHypRef Expression
1 pwex.1 . 2 𝐴 ∈ V
2 pwexg 4074 . 2 (𝐴 ∈ V → 𝒫 𝐴 ∈ V)
31, 2ax-mp 5 1 𝒫 𝐴 ∈ V
Colors of variables: wff set class
Syntax hints:  wcel 1465  Vcvv 2660  𝒫 cpw 3480
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 683  ax-5 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-10 1468  ax-11 1469  ax-i12 1470  ax-bndl 1471  ax-4 1472  ax-14 1477  ax-17 1491  ax-i9 1495  ax-ial 1499  ax-i5r 1500  ax-ext 2099  ax-sep 4016  ax-pow 4068
This theorem depends on definitions:  df-bi 116  df-tru 1319  df-nf 1422  df-sb 1721  df-clab 2104  df-cleq 2110  df-clel 2113  df-nfc 2247  df-v 2662  df-in 3047  df-ss 3054  df-pw 3482
This theorem is referenced by:  p0ex  4082  pp0ex  4083  ord3ex  4084  abexssex  5991  fnpm  6518  exmidpw  6770  npex  7249  axcnex  7635  pnfxr  7786  mnfxr  7790  ixxex  9650  istopon  12107  dmtopon  12117  fncld  12194  pw1dom2  13117
  Copyright terms: Public domain W3C validator